Melt butter in a medium skillet over medium-high heat. Add the leeks and cook, stirring often, until softened, about 6 minutes.
Season with salt and pepper, then add Dijon mustard, cream and 1 teaspoon rosemary.
Cook until the cream has reduced by half and the mixture is thick, about 5-8 minutes. Taste for seasoning and adjust as needed. Let cool completely.
When ready to assemble the galette, preheat the oven to 375° F and line a sheet pan with parchment paper.
Roll the dough out on a floured surface until it is about ¼ inch thick and 14-16 inches around.
Gently roll the dough up on to the rolling pin and transfer it to the center of the sheet pan. It should hang off the sides slightly.
Spread the cooled leek mixture evenly around the dough, leaving a 2 inch border on the outside.
Crumble goat cheese on top, then arrange the pears in a circular pattern. Sprinkle with remaining teaspoon of rosemary, salt, pepper and chopped walnuts.
Carefully gather the outer border of dough and fold it up and over the filling to form a 1-2 inch crust.
Brush the outer crust with egg wash if desired (this will produce a shinier, more golden crust).
Bake for 30-40 minutes or until the crust is golden brown. Let cool for 30 minutes before slicing.
Serve warm or at room temperature.